moongazer
If tan (theta) =5/4 and cos (theta) < 0 . Find the other trig. functions.
Could someone check my answers?
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moongazer
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am I right that theta is in quadrant 3 ?
Silent_Sorrow
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Yup, so Sin (theta) < 0 as well
moongazer
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Could you show your answers so that I can check my answers?
waterineyes
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No..
you should give your answers so that we can check..
Go ahead..
moongazer
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ok
moongazer
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\[\sin \theta =(-5\sqrt{41})/41\]
\[\cos \theta = (-4\sqrt{41})/41\]
\[\tan \theta = 5/4\]
\[\csc \theta = -\sqrt{41}/5\]
\[\sec \theta =-\sqrt{41}/4\]
\[\cot \theta = 4/5\]
moongazer
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Am I correct?
Silent_Sorrow
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|dw:1341743660142:dw|
Just remember "All Science Teachers Crazy" so in the first quad all trig functions are positive, in the 2nd all Sine functions are positive, in the 3rd all Tangent functions are positive so in the 4th all Cosine functions are positive.
moongazer
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Are all my answers correct?
moongazer
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Could someone check it?
moongazer
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@mathslover Are my answers correct?
mathslover
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when cos theta is negative then theta lies in 2nd quadrant ..
moongazer
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@mathslover why?
mathslover
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please wait
moongazer
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ok thanks :)
mathslover
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Remember this :Quadrant 1: Cosine is positive and Sine is positive.
(x > 0 ; y > 0) just as ( cos(theta) > 0 ; sin(theta) > 0)
Quadrant 2: Cosine is negative and Sine is positive.
(x < 0; y > 0) just as ( cos(theta) < 0 ; sin(theta) > 0)
Quadrant 3: Cosine is negative and Sine is negative.
(x < 0 ; y < 0) just as ( cos(theta) < 0 ; sin(theta)< 0)
Quadrant 4: Cosine is positive and Sine is negative.
( x > 0 ; y < 0 ) just as ( cos(theta) > 0 ; sin(theta) < 0)
mathslover
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@moongazer
moongazer
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I am here
mathslover
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So did u get that quadrant 2 : cos theta is negative ?
moongazer
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i'm still reading it :)
mathslover
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Take ur time
moongazer
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But in quadrant 3 cos theta is also negative so why I can't choose it as the location of theta?
moongazer
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isn't it that tan theta is positive in quadrant 3 and according to the given tan theta is positive.
So choosing that theta is in quadrant 3 is better?
mathslover
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oh yes u r also right but i am not perfect in this topic may be @lalaly do it for u
moongazer
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@lalaly My answers are correct right?
lalaly
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u can describe this as a right triangle
\[\tan (\theta)=\frac{opposite}{adjacent}=\frac{5}{4}\]so from this u know that opposite=5
and adjacent =4
|dw:1341746704835:dw|
lalaly
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now use those values to find the ratios for the other trig functions
moongazer
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But isn't it I can also view as|dw:1341747710304:dw|
moongazer
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Are my answers right or wrong?
ash2326
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@moongazer you are correct :D
moongazer
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@ash2326 Thanks for that!
ash2326
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you wanna see, the pic I made to check this?
moongazer
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ok, let me see it :)
ash2326
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here it is
moongazer
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That is also what I am thinking :)
ash2326
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Yay:D